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Popular Calculus >

integral of 3/x x^2

Solution

\int \frac{3}{x} x^{2} d x

Solution

\frac{3 x ^{2}}{2} + C

Solution steps

\int \frac{3}{x} x^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int \frac{1}{x} x^{2} d x

Simplify

\frac{1}{x} x^{2} : x

= 3 \cdot \int x d x

Apply the Power Rule

= 3 \cdot \frac{x ^{2}}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 x ^{2}}{2}

Add a constant to the solution

= \frac{3 x ^{2}}{2} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of 3/x x^2 ?
The integral of 3/x x^2 is (3x^2)/2+C